28. chen.huang:23:superlinear#
Superlinear stochastic heat equation on \(\mathbb{R}^d\)
Le Chen and Jingyu Huang
Abstract: In this paper, we study the stochastic heat equation (SHE) on \(\mathbb{R}^d\) subject to a centered Gaussian noise that is white in time and colored in space. We establish the existence and uniqueness of the random field solution in the presence of locally Lipschitz drift and diffusion coefficients, which can have certain superlinear growth. This is a nontrivial extension of the recent work by Dalang, Khoshnevisan and Zhang [DKZ19], where the one-dimensional SHE on \([0,1]\) subject to space-time white noise has been studied.
MSC 2010 subject classifications: Primary. 60H15; Secondary. 35R60.
Keywords: global solution, stochastic heat equation, reaction-diffusion, Dalang’s condition, superlinear growth.
[CH23b] Chen, Le & Huang, Jingyu (2023) ‘Superlinear stochastic heat equation on $mathbb{R}^d$’, Proc. Amer. Math. Soc. 151, 4063–4078. <https://doi.org/10.1090/proc/16436>
@article{chen.huang:23:superlinear,
author = {Chen, Le and Huang, Jingyu},
title = {Superlinear stochastic heat equation on {$\Bbb{R}^d$}},
journal = {Proc. Amer. Math. Soc.},
fjournal = {Proceedings of the American Mathematical Society},
volume = {151},
year = {2023},
number = {9},
pages = {4063--4078},
issn = {0002-9939},
mrclass = {60H15 (35K57 35R60)},
mrnumber = {4607649},
doi = {10.1090/proc/16436},
url = {https://doi.org/10.1090/proc/16436}
}
References: Balan and Chen [BC18]; Chen and Dalang [CD15b]; Chen and Eisenberg [CE22b]; Chen and Huang [CH19a]; Chen and Kim [CK19]; Conus and Khoshnevisan [CK12]; Da Prato and Zabczyk [DPZ14]; Dalang et al. [DKM+09]; Dalang [Dal99]; Dalang et al. [DKZ19]; Fernández Bonder and Groisman [FBG09]; Foondun and Nualart [FN21]; Huang [Hua17]; Millet and Sanz-Solé [MSS21]; Salins [Sal21]; Sanz-Solé and Sarrà [SSS02]; Walsh [Wal86];